The present invention relates to methods and apparatus for digitally storing and reconstructing analog waveforms and, more particularly, to an electronic musical instrument using such apparatus and methods for generating audio waveforms which are percussive in nature having an envelope which decays gradually with time.
It is known to construct an electronic musical instrument using a digital memory in which an audio waveform is stored in a sampled form. The stored audio waveform is conventionally read out of the memory at a constant rate in response to an address counter and is then converted to an analog form by a digital to analog converter. The analog signal may subsequently be used to supply or drive a suitable output system for producing a corresponding musical tone.
In systems of the foregoing type, it is desirable to store the digital samples using as few binary bits as possible in order to minimize the cost of the memory. Thus, in the case of periodic waveforms, it is common to store digital samples defining only one period of the waveform, the remainder of the waveform being derived through calculations performed on the stored samples. Audio waveforms which are not periodic in nature, such as complex percussive waveforms which decay gradually with time, cannot, however, be treated in this manner. In particular, in order to faithfully reproduce such waveforms using the sequential sampling technique described above, it is necessary to store substantially the entire waveform in sampled form.
The signal to quantizing noise ratio characterizing sequentially sampled systems of the foregoing type is given by the expression 20 log (% of full scale used.times.2.sup.n), where n is the number of bits characterizing the system. In other words, the signal to quantizing noise ratio is proportional to the word length of the memory and to the percentage of the full dynamic range of the word length use. Thus, for example, increasing the word length by one bit will raise the ratio by 6 db whereas reducing the wavefrom from full scale to half scale will decrease the ratio by 6 db. Therefore, in the case of a percussive waveform, the signal to noise ratio will continuously decrease as the waveform decays.
It has heretofore been considered necessary to use at least 12-bit word lengths in order to achieve an adequate signal to noise ratio (72 db for most audio waveforms) in sequentially samples systems of the foregoing type. It is a primary object of the present invention to provide a technique, which is particularly useful in association with percussive type waveforms, whereby the bit word length used by the memory may be substantially reduced from this number without adversely affecting the average signal to noise ratio characterizing the lower level signals.